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A functional equation for invariant-image is presented and solved to identify the largest group of image-preserving weight transformations for the rational Bezier triangles. A fundamental theorem on the invariants of Lie group actions is used to demonstrate that \(\frac{1}{2}(n+1)(n+2)-3\) real-valued, functionally-independent invariants exist for the degree \(n\) triangles. Explicit forms of the real-valued invariants are derived; and a further, discrete-valued, invariant is identified and shown to complete the set required for invariant image.

Cast shadows need careful consideration in the development of robust dynamic scene analysis systems. Cast shadow detection is critical for accurate object detection in video streams, and their misclassification can cause errors in segmentation and tracking. Many algorithms for shadow detection have been proposed in the literature; however a complete, comparative evaluation of existing approaches is lacking. This paper presents a comprehensive survey of shadow detection methods, organised in a novel taxonomy based on object/environment dependency and implementation domain. In addition a comparative evaluation of representative algorithms, based on quantitative and qualitative metrics is presented to evaluate the algorithms on a benchmark suite of indoor and outdoor video sequences.

A generalization of Patterson's work on the invariants of the rational Bezier curves, to the case of weight vectors of mixed-sign is presented. It is shown that an additional invariant is required in the general case. The results are viewed from the perspective of the Fundamental Theorem on invariants for Lie groups.

The authors extend their previous work on Ultrasound (US) image lesion detection and segmentation, to classification, proposing a complete end-to-end solution for automatic Ultrasound Computer Aided Detection (US CAD). Carried out is a comprehensive analysis to determine the best classifier-feature set combination that works optimally in US imaging. In particular the use of nineteen features categorised into three groups (shape, texture and edge), ten classifiers and 22 feature selection approaches are used in the analysis. From the overall performance, the classifier RBFNetworks defined by the WEKA pattern recognition tool set, with a feature set comprising of the area to perimeter ratio, solidity, elongation, roundness, standard deviation, two Fourier related and a fractal related texture measures out-performed other combinations of feature-classifiers, with an achievement of predicted Az value of 0.948. Next analyzed is the use of a number of different metrics in performance analysis and provide an insight to future improvements and extension. DOI: 10.4018/jcmam.2010040104 54 International Journal of Computational Models and Algorithms in Medicine, 1(2), 53-81, April-June 2010 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. (CAD) systems with high sensitivity, specificity and consistency. Despite these efforts CAD of ultrasound images still remains an area with many open research problems that needs solutions. In this article we identify a key open research problem in ultrasound imaging which is thoroughly investigated in order to develop a new method of ultrasound image processing for extracting relevant tissue structure information that will help differentiate between normal and malignant tissues. The ultimate goal is to provide fast and reliable tools for the early detection of malignant tissues in ultrasound images. The current practical use of a typical US CAD system can be illustrated as in figure 1. The input of a CAD system consists of a rectangular region of interests, manually selected by a radiologist. The output provides a statistical analysis that can aid the radiologist in the final decision making, i.e., the malignancy and/or type of cancer. The above approach (Figure 1) to CAD of breast ultrasound images has a limitation in that no aid is provided to the radiologist who selects the Region of Interest (ROI) of the lesions. Modern computer vision approaches can be used for fully automatic initial lesion detection, which can then be used as an aid to the decision making process of the radiologist, thus improving the accuracy of their performance. Further at this initial stage the need of a radiologist can be completely eliminated by allowing for a higher degree of false positives which can later be removed by further CAD or the presence of a radiologist at the final decision making stage. Thus in this article we aim to use our previous work in initial lesion detection and segmentation to remove the need of a radiologist at the initial lesion detection stage and then propose a novel approach for the selection of lesion features and feature based lesion classification to automatically determine the lesion type. In particular within the research context of this article we aim to develop a framework for the selection of best feature-classifier combinations in US breast imaging. To the authors knowledge such an attempt has previously not been published in relevant literature. The aims of our research are: (i) to automate the Region of Interest (ROI) selection and (ii) to improve the segmentation and classification algorithms. Figure 2 illustrates the above aims. It is important to note that both above automations will improve the information provided to the radiologist to aid in decision making (at the ROI cropping and final decision making stages, refer to Figure 1), improving the overall accuracy of the CAD system and reducing human error. For clarity of presentation this article has been divided into 5 sub-sections. Apart from this section which provides the reader an introduction to the problem domain and setting out the objectives of the proposed research, State-ofthe-art US CAD Systems section introduces a detailed review of the state-if-the-art in US CAD system research. Method section proposes the proposed end-to-end solution to US CAD, with particular emphasis given to the recognition stage. Experimental results and analysis section Figure 1. Existing US CAD approach 27 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the publisher's webpage: www.igi-global.com/article/computer-aided-detectionrecognition-lesions/43021

This paper proposes a novel approach to initial lesion detection in ultrasound breast images. The objective is to automate the manual process of region of interest (ROI) labeling in computer‐aided diagnosis (CAD). We propose the use of hybrid filtering, multifractal processing, and thresholding segmentation in initial lesion detection and automated ROI labeling. We used 360 ultrasound breast images to evaluate the performance of the proposed approach. Images were preprocessed using histogram equalization before hybrid filtering and multifractal analysis were conducted. Subsequently, thresholding segmentation was applied on the image. Finally, the initial lesions are detected using a rule‐based approach. The accuracy of the automated ROI labeling was measured as an overlap of 0.4 with the lesion outline as compared with lesions labeled by an expert radiologist. We compared the performance of the proposed method with that of three state‐of‐the‐art methods, namely, the radial gradient index filtering technique, the local mean technique, and the fractal dimension technique. We conclude that the proposed method is more accurate and performs more effectively than do the benchmark algorithms considered. PACS numbers: 87.57.Nk

Dupin cyclides, their applications in geometric modelling and their parametrization using bi-quadratic patches bounded by lines of curvature, have been investigated in recent years by a number of authors such as Martin, de Pont and Sharrock in 1986, Boehm in 1990, Pratt in 1990, and Degen in 1994. However, no completely reliable and general algorithm for the determination of bi-quadratic cyclide patches has appeared in the literature. This paper presents a new approach that produces any required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic geometric constraints or restrictions. Specifically, if a bi-quadratic parametrization exists for the specified region of the cyclide, then it is correctly determined. Explicit formulae are given for the Bernstein weights and vectors of the parametrizations. The method is neither cyclide specific nor specific to the construction of bi-quadratic rational parametrizations-it may therefore be applied to other surfaces and to higher degree rational constructions.

In this paper, we propose a fast DWT-based multi-resolution texture synthesis algorithm in which coefficient blocks of the spatio-frequency components of the input texture are efficiently stitched together to form the corresponding components of the synthesised output texture. We propose the use of an automatically generated threshold to determine the visually significant coefficients, which act as elements of a matching template used in the texture quilting process. We show that the use of a limited set of visually significant coefficients, regardless of their level of resolution, not only reduces the computational cost, but also results in more realistic texture synthesis. A transform domain texture blending strategy is used to remove the remaining artefacts across edges, improving the synthesised texture quality further. We use popular test textures to compare our results with that of the state-of-the-art techniques. Some application scenarios of the proposed algorithm are also discussed.

The present generation of Ambient Light Sensors (ALS) of a mobile handheld device suffer from two practical shortcomings. The ALSs are narrow angle, i.e. they respond effectively only within a narrow angle of operation and there is a latency of operation. As a result mobile applications that operate based on the ALS readings could perform sub-optimally especially when operated in environments with non-uniform illumination. The applications will either adopt with unacceptable levels of latency or/and may demonstrate a discrete nature of operation. In this paper we propose a framework to predict the ambient illumination of an environment in which a mobile device is present. The predictions are based on an illumination model that is developed based on a small number of readings taken during an application calibration stage. We use a machine learning based approach in developing the models. Five different regression models were developed, implemented and compared based on Polynomial, Gaussian, Sum of Sine, Fourier and Smoothing Spline functions. Approaches to remove noisy data, missing values and outliers were used prior to the modelling stage to remove their negative effects on modelling. The prediction accuracy for all models were found to be above 0.99 when measured using R-Squared test with the best performance being from Smoothing Spline. In this paper we will discuss mathematical complexity of each model and investigate how to make compromises in finding the best model.

Inflammatory muscle disease is a group of rare idiopathic conditions that cause progressive skeletal muscle weakness. Diagnosis typically requires an assortment of clinical tests, including magnetic resonance imaging (MRI) of the thigh muscles to assess fat infiltration and inflammation. We hypothesise that features from multi-spectral MRI can accurately predict patient diagnosis, without the need for additional tests. A novel method is presented using computer-extracted features of the T1-STIR bivariate histogram to detect disease. The dataset comprised of 78 image-pairs from 8 patients with inflammatory muscle disease symptoms and 61 image-pairs from 9 control cases with no disease. T1 and STIR slices were co-registered and the background discarded. A feature vector was designed to measure the distribution of standardised intensity values (e.g. standard deviation, kurtosis, gini) for the muscle, fat, and leg regions of the bivariate histogram. Feature dimensionality was reduced using a combined leave-one-out and k-folds cross-validation method to select the most important features. A Bayes network was trained to predicted patient diagnosis on a per-slice basis, 10- fold cross-validated. The system attained 92% sensitivity and 82% specificity (ROC area 0.93). These results support the hypothesis that accurate diagnosis of inflammatory muscle disease is possible using MRI alone, without the need for additional clinical tests, with the potential benefit of faster diagnosis and better care for patients with this group of rare conditions.

In this article we propose a multiresolution texture synthesis algorithm in which coefficient blocks of the spatiofrequency components of the input texture are efficiently stitched together to form the corresponding components of the synthesized output texture. We propose two algorithms to this effect. In the first, we use a constant block size throughout the algorithm. In the second, we adaptively split blocks so as to use the largest possible block size in order to preserve the global structure, while maintaining the mismatched error of the overlapped boundaries below a certain error tolerance. Throughout the algorithm designs, special consideration is given to minimizing the computational cost. We show that the adaptation of the multiresolution approach results in a fast, cost effective, flexible texture synthesis algorithm that is capable of being used in conjunction with modern, bandwidth-adaptive, Markov random field imaging applications. A collection of regular and stochastic test textures is used to prove the effectiveness of the proposed algorithm.

A novel technique for the construction of positive weight high-precision rational approximations to a class of transcendental curves is presented. The approximations are induced from the rational parametrisations of the circle. The previously published rational parametrisations of the circle are not suited to the induction process and the new parametrisations are constructed in the paper for the purpose. Explicit rational approximations of a number of transcendental curves are then given. The work is a development of the authors’ previous work on induced rational parametrisations of special algebraic curves.

In this paper, we propose a novel, discrete wavelet transform (DWT) domain implementation of our previously proposed, pioneering block-based disparity compensated predictive coding algorithm for stereo image compression. Under the present research context we perform predictive coding in the form of pioneering block search in the sub-band domain. The resulting transform domain predictive error image is subsequently converted to a so-called wavelet-block representation, before being quantized and entropy coded by a JPEG-like CODEC. We show that the proposed novel implementation is able to effectively transfer the inherent advantages of DWT-based image coding technology to efficient stereo image pair compression. At equivalent bit rates, the proposed algorithm achieves peak signal to noise ratio gains of up to 5.5 dB, for reconstructed predicted images, as compared to traditional and state of the art DCT and DWT-based predictive coding algorithms.

Rational parametrisation of curves and surfaces is a defacto industry standard for computer graphics and shape representation. While it is well known that rational parametrisations of the conic sections exist, and their explicit forms are used in geometric modeling (Hoschek and Lasser, 1993), other classical curves for which rational parametrisations may be determined have received less attention in the literature. This paper presents an elegant method for the explicit computation of rational parametrisations for many 'special' or famous curves. The technique 'induces' a parametrisation of a 'higher' or 'target' curve from a 'primitive' or 'source' curve for which rational parametrisations are known - e.g., the straight line and the conic sections. A number of examples and modeling applications are given.

The paper considers a particular general class of parametrised path function used in computer graphics, geometric modeling and approximation theory. General methods are developed for the identification of the conditions under which parameter transformations preserve the path geometry. The determination of these 'parameter symmetries' is shown to be equivalent to the identification of the solution space of a functional equation. Case studies, each with distinctive features, are presented to illustrate the concepts developed and the generality of the approach. Full solutions are obtained and seen to provide both known and new results.

A CAD tool for the garment industry is described. The tool generates garment patterns using Bézier curves and is currently embedded within an intelligent knitwear design support system. The curves fulfil the design constraints imposed by the domain, are adaptable to individual styles and enable intuitive manipulation by the user. The system described is designed primarily to provide a means of improved communication between designers and technicians but it has the potential to become a key component in a bespoke design system.

A new set of colour appearance data was obtained from a series of experiments in which 240 wool samples having a large size of 3 x 3 in. square that subtends 10° at the observer's eye, and covering a large colour gamut were used. Each colour was assessed by a panel of five observers using a magnitude estimation method under three light sources, D65, TL84, and A. In total, 10,770 estimations were made, and these form a set of new colour appearance data in textiles. Data analysis was carried out and shows that the accuracy of the visual results for different observers is quite good. the colour appearance data were used to test the performance of seven chromatic-adaptation transformations, i.e., BFD, Bartleson, von Kries, CIE, Hunt, CIEL*a*b*, and Fairchild. the results show that the BFD transformation gives the most accurate prediction to the visual results between all transformations studied. All transformations can have a better fit to the experimental grid under TL84 than that under A. However, the results given by the best chromatic-adaptation transformation are still unsatisfied in colour industries, especially in the textile industry. the two sets of experimental grids respectively derived from this work and by Luo et al. (1991) were also studied. an expected difference between the two sets of experimental grids was found. the difference may mainly result from two factors: the experimental method in assessment and the size of the samples. © 1995 John Wiley & Sons, Inc.

With the wide availability of general purpose parallel computers, there is a need to reconsider hidden surface elimination (HSE) algorithms with respect to parallel implementation. This paper considers MIMD parallel implementations off our common image space HSE algorithms - recursive subdivision, scan line, painter's, and z-buffer. Their suitability for parallel implementation is investigated and their relative performance in multiprocessor systems is measured using polygonal scene descriptions of between 200 and 2500 polygons. Dependence on the size of scene description is measured and results are extrapolated to larger scene descriptions. It is shown that HSE algorithms may be efficiently parallelised. A distributed z-buffer is shown to be a fast and efficient method of solving HSE problems using parallel computers.

This paper presents a case based reasoning approach for making profit in the foreign exchange (forex) market with controlled risk using k nearest neighbour (kNN) and improving on the results with neural networks (NNs) and a combination of both. Although many professionals have proven that exchange rates can be forecast using neural networks for example, poor trading strategies and unpredictable market fluctuation can inevitably still result in substantial loss. As a result, the method proposed in this paper will focus on predicting the outcome of potential trades with fixed stop loss (ST) and take profit (TP) positions1, in terms of a win or loss. With the help of the Monte Carlo method, randomly generated trades together with different traditional technical indicators are fed into the models, resulting in a win or lose output. This is clearly a case based reasoning approach, in terms of searching similar past trade setups for selecting successful trades. There are several advantages over classical forecasting associated with such an approach, and the technique presented in this paper brings a novel perspective to problem of exchange trades predictability. The strategies implemented have not been empirically investigated with such wide a range of time granularities as is done in this paper, in any to the authors known academic literature. The profitability of this approach is back-tested at the end of this paper and highly encouraging results are reported.

We propose a novel approach to fully automatic lesion boundary detection in ultrasound breast images. The novelty of the proposed work lies in the complete automation of the manual process of initial Region-of-Interest (ROI) labeling and in the procedure adopted for the subsequent lesion boundary detection. Histogram equalization is initially used to pre-process the images followed by hybrid filtering and multifractal analysis stages. Subsequently, a single valued thresholding segmentation stage and a rule-based approach is used for the identification of the lesion ROI and the point of interest that is used as the seed-point. Next, starting from this point an Isotropic Gaussian function is applied on the inverted, original ultrasound image. The lesion area is then separated from the background by a thresholding segmentation stage and the initial boundary is detected via edge detection. Finally to further improve and refine the initial boundary, we make use of a state-of-the-art active contour method (i.e. gradient vector flow (GVF) snake model). We provide results that include judgments from expert radiologists on 360 ultrasound images proving that the final boundary detected by the proposed method is highly accurate. We compare the proposed method with two existing state-of- the-art methods, namely the radial gradient index filtering (RGI) technique of Drukker et. al. and the local mean technique proposed by Yap et. al., in proving the proposed method's robustness and accuracy.

Progressive texture synthesis can provide an added functional advantage to existing texture synthesis algorithms, which are time consuming and fail to deliver in some application areas. To provide practical solutions to this challenge we have previously proposed a discrete wavelet transform (DWT) based texture synthesis algorithm for 2D surfaces. In this paper we propose the extension of this approach to 3D progressive-texture synthesis. The proposed 3D progressive- texture synthesis algorithm makes use of the EZW (embedded zero-tree wavelet) idea proposed by Shapiro, which is capable of prioritising the coefficients of a DWT decomposed image according to their visual significance. We demonstrate the use of the proposed algorithm on progressive texturing geometric surfaces such as ring dupin cyclides, toruses, spheres, parametrised by rational Bezier patches. We provide experimental results to prove the effectiveness of the proposed approach, when synthesising textures of regular, irregular and stochastic nature. Further experimental results are provided to illustrate the practical use of the proposed progressive texture synthesis algorithm in resource constrained application domains. (10 pages)

The use of shape-adaptive transforms is a popular approach for coding arbitrarily shaped objects in image/video coding due to their adaptability at object edges and low complexity. In this respect shape adaptive DCT (SA-DCT) and shape adaptive DWT (SA-DWT) have been proposed in previous literature. The Integer Transform (IT), a derivative of the 4x4 DCT, has been adopted in the latest H.264/AVC standard for coding image blocks in residual data (texture). The associated integer arithmetic guarantees fast and accurate coding/decoding. In this paper, we propose a novel Shape Adaptive Integer Transform (SA-IT) which can be effectively used in future for enabling arbitrary shaped object coding in H.264. Though Integer Transforms are a derivative of 4x4 DCTs, in H.264, to maintain integer arithmetic capability, the post-and pre-scaling factors of transform process are integrated into the forward and inverse quantiser stages respectively for reducing the total number of multiplications and avoiding the loss of accuracy. Thus SA-IT considerably differs from SA-DCT and calls for novel design and implementation considerations based on combining those merits of both SA-DCT and IT. We provide theoretical proofs and support them with experimental justifications.

Several shadow detection and removal algorithms have been proposed to distinguish between objects and their shadows for computer vision applications, as the design of a fast and efficient algorithm remains a challenge. In this work, based on a physically-derived hypothesis for shadow identification, novel, simple and fast shadow detection algorithms are proposed and implemented in the spatial (pixel) and frequency (Fourier) domains. It is shown that the algorithms effectively remove shadows under various lighting and environmental conditions. The proposed algorithms are able to detect shadows in both umbra and penumbra neighborhoods.

Human visual system (HVS) is able to capture, process and record images with high dynamic range of luminosity, colour and focus. Unfortunately general purpose digital cameras suffer from limitations of their dynamic ranges and are thus unable to produce visually optimized photographic images. The approach used to resolve this problem is to capture images of the same scene using different exposure and focus settings and to use software based post processing technique to fuse the resulting images. Post processing techniques in general suffer from the fact that the fusion is done on already encoded images, which are decoded for the application of the pixel domain fusion techniques. The coding losses in the multiple exposure images lead to algorithmic loss in fusion, and hence would best be avoided. In this paper we propose an algorithm to perform fully automatic multi-exposure/focus image fusion in discrete cosine transform (DCT) domain. We show that fusion in DCT domain enables efficient fusion of lossless image data and the algorithm's use as an in-camera solution. This is the first attempt in addressing the problem of image fusion in transform domain. The results are compared with that of the existing state-of-the art algorithms.

We propose an extension to the H.264 video coding standard, which is capable of efficiently coding stereoscopic video sequences. In contrast to previous techniques, the proposed Stereoscopic Video CODEC uses a single modified H.264 encoder and a single modified H.264 decoder in its design. The left (reference) and right (predicted) sequences are fed alternatively to the encoder. The modified H.264 encoder uses a Decoded Picture Buffer Store (DPBS) in addition to the regular DPB of the original H.264 encoder. An effective buffer management strategy between DPBS and DPB is used so that the left sequence frames are coded only based on its previously coded frames while the right frames are coded based on previously coded frames from both left and right sequences. We show that the proposed CODEC has the capability of exploiting worldline correlation present in stereo video sequences, in addition to the exploitation of joint spatial-temporal-binocular correlation. Further we show that the coded bit stream fully conforms to a standard H.264 bit-stream and a standard H.264 decoder will be able to effectively decode the left video stream ignoring the right. We provide experimental results on two popular test stereoscopic video sequences to prove the efficiency of the proposed CODEC.

In this paper we propose a fast DWT based multi-resolution texture synthesis algorithm in which coefficient blocks of the spatio-frequency components of the input texture are efficiently stitched together (quilted) to form the corresponding components of the synthesised output texture. We propose the use of an automatically generated threshold to determine the significant coefficients, which acts as elements of a matching template used in the texture quilting process. We show that the use of a limited set of visually significant coefficients, regardless of their level of resolution, not only reduces the computational cost, but also results in more realistic texture synthesis. The blending strategy used removes remaining artefacts across edges improving the quality further. We use popular test textures to compare our results with the existing state-or-the-art techniques. Many application scenarios of the proposed algorithm are also discussed.

In this paper we propose a fast DWT based multi-resolution texture synthesis algorithm in which coefficient blocks of the spatio-frequeny components of the input texture are efficiently stitched together (quilted) to form the corresponding components of the synthesised output texture. We propose the use of an automatically generated threshold to determine the significant coefficients which acts as elements of a matching template used in the texture quilting process. We show that the use of a limited set of, visually significant coefficients, regardless of their level of resolution, not only reduces the computational cost, but also results in more realistic texture synthesis. We use popular test textures to compare our results with that of the existing state-or-the-art techniques. Many application scenarios of the proposed algorithm are also discussed.

In this paper we propose a stereo image CODEC, that uses overlapped block disparity estimation/compensation in multiresolution wavelet transform domain. Overlapped block matching is known to be able to reduce blocking artifacts by linearly combining multiple blocks provided by the disparity vectors of a block and its neighbours. This capability of OBM and discrete wavelet transform's (DWT) versatile time-frequency localization is expected to improve rate distortion performance. With the proposed CODEC gains of up to 1 dB at low bit rates as compared to the benchmark of S. Sethuraman et al. (1994) used in the paper.

The current trends in computer animations, virtual reality and augmented reality applications have resulted in the problem of texture synthesis receiving considerable attention from the computer graphics and image processing research community. In this paper we revisit the well-known texture synthesis method, image quilting, first proposed by Efros and Freeman and propose improvements to its algorithms and implementation. Further, we outline its application within a multiresolution framework, particularly suited for modern imaging applications associated with compressed image data. We provide experimental results to prove the effectiveness of the proposed modifications and variation.

Block based texture synthesis algorithms have shown better results than others as they help to preserve the global structure. Previous research has proposed several approaches in the pixel domain, but little effort has been taken in the synthesis of texture in a multiresolution domain. We propose a multiresolution framework in which coefficient-blocks of the spatio-frequency components of the input texture are efficiently stitched together to form the corresponding components of the output texture. We propose two algorithms to this effect. In the first, we use a constant block size throughout the algorithm. In the second, we adaptively split blocks so as to use the largest possible block size in order to preserve the global structure, while maintaining the mismatched error of the overlapped boundaries below a certain error tolerance. Special consideration is given to minimization of the computational cost, throughout the algorithm designs. We show that the adaptation of the multiresolution approach results in a fast, cost-effective, flexible texture synthesis algorithm that is capable of being used in modern, bandwidth-adaptive, real-time imaging applications. A collection of regular and stochastic test textures is used to prove the effectiveness of the proposed algorithm.

A path algebra and its applications in computer graphics and modeling is introduced. The emphasis is on concepts and applications rather than complete mathematical details. The algebra can be used either as a design tool or as a means of constructing rational parametrisations of curves and surfaces compatible with most current modeling and visualisation systems. A number of examples are given.

We propose a novel stereo image coding technique, which uses an architecture similar to that of a discrete cosine transform (DCT) based baseline JPEG-CODEC (Pennebaker and Mitchell, 1993), but effectively replaces the DCT technology by the more recently popularized discrete wavelet transform (DWT) technology. We show that as a result of this hybrid design, which combines the advantage of two popular technologies, the proposed CODEC has improved rate distortion and subjective image quality performance as compared to DCT based stereo image compression techniques (Perkins, 1992). In particular, at very low bit rates (0.15 bpp), we report peak-signal-to-noise-ratio (PSNR) gains of up to 3.66 dB, whereas at higher bit rates we report gains in the order of 1 dB.

In this paper we propose the wavelet domain implementation of our original pioneering block based stereo image compression algorithm and compare its performance with traditional, DCT based and state-of-the-art, DWT based stereo image compression algorithms. Due to the special requirements of the pioneering block based CODEC and the properties of DWT based multi-resolution decomposition, the implementation of the original algorithm in the wavelet domain is not straightforward and thus provides knowledge and understanding of significant novelty. Experiments were performed on a set of eight stereo image pairs representing, natural, synthetic, in-door and out-door images. We show that for the same bit rates, objective quality gains of up to 5 dB (PSNR) are obtained as compared to the benchmark algorithms. One significant property of the proposed CODEC is its ability to produce reconstructed right images of up to 25 dB at right image bit rates as low as 0.1 bpp. Significant gains in subjective image quality are also obtained as compared to benchmark methods.

The paper considers a particular general class of parametrised path functions used in computer graphics, geometric modeling and approximation theory for the construction of curves and surfaces. General methods are developed for the identification of the conditions under which parameter transformations preserve the path geometry. The determination of these ‘parameter symmetries’ is shown to be equivalent to the identification of the solution space of a functional equation.

Many parametric curve and surface methods, including polynomial and spline, require sets of `parameter’ functions to be specified in addition to control-, or interpolation-point sets. It is shown here that symmetry is a powerful tool for the analysis of this class of curve function and can, for example, be applied to provide complete answers to fundamental questions such as: (i) if the control point set is held fixed, under what conditions do different sets of parameter functions determine the same curve?

In this paper, we propose a novel object driven, block based algorithm for the compression of stereo image pairs. The algorithm effectively combines the simplicity and adaptability of the existing block based stereo image compression techniques with an edge/contour based object extraction technique to determine appropriate compression strategy for various areas of the right image. Extensive experiments carried out support that significant improvements of up to 20% in compression ratio can be achieved by the proposed algorithm, compared with the existing stereo image compression techniques. Yet the reconstructed image quality is maintained at an equivalent level in terms of PSNR values. In terms of visual quality, the right image reconstructed by the proposed algorithm does not incur any noticeable effect compared with the outputs of the best algorithms. The proposed algorithm performs object extraction and matching between the reconstructed left frame and the original right frame to identify those objects that match but are displaced by varying amounts due to binocular parallax. Different coding strategies are then applied separately to internal areas and the bounding areas for each identified object. Based on the mean squared matching error of the internal blocks and a selected threshold, a decision is made whether or not to encode the predictive errors inside these objects. The output bit stream includes entropy coding of object disparity, block disparity and possibly some errors, which fail to meet the threshold requirement in the proposed algorithm.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.